Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets: 20 - Brossura

Brossura

ISBN 10: 9048163781 ISBN 13: 9789048163786

Casa editrice: Springer, 2010

Riassunto

This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan­ dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish­ ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand­ book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand­ book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem­ inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti­ eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

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Contenuti

Volume Contributors. Preface. Introduction. I: Topological Structures in Fuzzy Sets. 1. Uniform Completion in Pointfree Topology; B. Banaschewshi. 2. Monadic Convergence Structures; W. Gähler. 3. A Unified Approach to the Concept of Fuzzy L-Uniform Space; J. Gutiérrez Garcí, M.A. de Prada Vicente, A.P. Sostak. 4. Many Valued Topologies and Borel Probability Measures; U. Höhle. 5. Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions; T. Kubiak. 6. Lattice-Valued Frames, Functor Categories and Classes of Sober Spaces; A. Pultr, S.E. Rodabaugh. Appendix to Chapter 6: Weakening the Requirement that L be a Complete Chain; U. Höhle, S.E. Rodabaugh. 7. Axiomatic Foundations for Uniform Operator Quasi-Uniformities; S.E. Rodabaugh. 8. Full Fuzzy Topology; L.N. Stout. II: Algebraic Structures in Fuzzy Sets. 9. Fuzzy Logics Arising from Strict De Morgan Systems; M. Gehrke, C. Walker, E. Walker. 10. Structure of Girard Monoids on [0,1]; S. Jenei. 11. On the Geometry of Choice; C.J. Mulvey. 12. On Some Fuzzy Categories Related to Category LTOP of L-Topological Spaces; A.P. Sostak. III: Related Topics in Topological and Algebraic Structures. 13. Fuzzy Compactness via Categorical Closure Operators; I.W. Alderton. 14. Discrete Triangular Norms; B. de Baets, R. Mesiar. 15. Powerset Operators Based Approach to Fuzzy Topologies on Fuzzy Sets; C. Guido. 16. Lifting of Sobriety Concepts with Particular Reference to (L,M)-Topological Spaces; W. Kotzé. 17. Examples for Different Sobrieties in Fixed-Basis Topology; A. Pultr, S.E. Rodabaugh. 18. Additive Generators of Non-Continuous Triangular Norms; P. Viceník. 19. Groups, T-Norms and Families of De Morgan Systems; C. Walker, E. Walker.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 9048163781
• ISBN 13: 9789048163786
• Rilegatura: Copertina flessibile
• Numero di pagine: 484
• Redattore: Rodabaugh S.E., Klement Erich Peter
• Contatto del produttore: non disponibile
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